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THISTLETHWAITE'S THEOREM FOR VIRTUAL LINKS

SERGEI CHMUTOV

The Ohio State University, Mansfield, 1680 University Drive, Mansfield, OH 44906, USA

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and

JEREMY VOLTZ

Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

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https://doi.org/10.1142/S0218216508006609Cited by:27 (Source: Crossref)

Abstract

The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded into a (higher genus) surface. For such graphs we use the generalization of the Tutte polynomial discovered by Bollobás and Riordan.

Keywords:

AMSC: 57M15, 57M25, 57M27, 05C10

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